Grey relational analysis based optimization of process parameters for ultrasonic slitting of glass 2

Scientific Journal of Impact Factor (SJIF): 3.134

E-ISSN (O): 2348-4470 P-ISSN (P): 2348-6406

International Journal of Advance Engineering and Research Development Volume 2,Issue 12,December -2015

Grey Relational Analysis Based Optimization of Process Parameters for Ultrasonic Slitting of Glass A. B. Pandey1, H. C. Jakharia2, R. S. Agarwal3, B. R. Dave4 1,3

Department of Mechanical Engineering, Faculty of Technology & Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India.

2 Government Polytechnic, Rajkot 4 Mechanical Engineering Department, KJIT, Savli, Vadodara

Abstract —Ultrasonic machining is extremely popular for machining of brittle materials like glass, ceramics etc. Various optical and other applications require slitting of glass. In this work, a full factorial experiment is designed to study the effect of process parameters on ultrasonic slitting of glass. The control parameters selected include amplitude, pressure and thickness of the glass sheet being machined. Three levels of each of these parameters are selected giving 33 = 27 trials. The material removal rate (MRR), overcut (OC) and taper produced on the glass while slitting are measured as response parameters. Ultrasonic machining is a complex process to control and get desired machining results. Grey relational analysis is applied to the experimental output data in order to determine the best combination of input parameters for different cutting requirements like roughing, semi-finishing and finishing. Parameter combinations are graded using grey relational analysis (GRA) process and the optimum combination is suggested for various requirements of machiningin terms of roughing, semi-finishing and finishing.

Keywords-Ultrasonic Slitting, Optimization, Grey Relational Analysis I. INTRODUCTION Traditional ceramics and glasses are extensively used to manufacture many products. Advanced ceramics have been widely adopted as functional as well as structural engineering materials [1]. Ultrasonic machining offers a solution to the expanding need for machining brittle materials such as single crystals, glasses and polycrystalline ceramics, and for increasing complex operations to provide intricate shapes and workpiece profiles. This machining process is non-thermal, non-chemical, creates no change in the microstructure, chemical or physical properties of the workpiece and offers virtually stress-free machined surfaces. It is therefore used extensively in machining hard and brittle materials that are difficult to cut by other conventional methods [2]. Generation of slits in glass is required in variety of applications like optical microscopes, measurement optics etc. In order to produce these components, ultrasonic machining is a viable alternative. For machining to required dimensions, the setting of process parameters to appropriate value is extremely necessary.

Since, optimizing multiple output qualities of a process requires the calculation of a grey relational analysis (GRA) is used to integrate and optimize the multiple output qualities of a process [3–5]. Many papers have presented the effective method and proven its usefulness in various applications [6-8].

In this paper, the experimental data as an outcome of experiments on producing slits using ultrasonic process on common glass is analyzed using grey relational analysis to find the optimum process parameters.

II. ULTRASONIC SLITTING EXPERIMENTS A full factorial design of experiment with replication is used with three control factors – amplitude, pressure and thickness of the glass sheet. The values selected for the low, medium and high level for each of the control parameters is mentioned in Table 1. The amplitude is varied in terms of percentage of amplitude delivered at full power by the converter.

Table 1. Parameters and their Levels Amplitude A1 = 70% A2 = 80% A3 = 90%

Pressure P1 = 0.5 bar P2 = 2 bar P3 = 3.5 bar

Glass Thickness t1 =1.23 mm t2 =2.16 mm t3 = 3.12 mm

Material removal rate (MRR), overcut (OC) and taper generated during slitting are taken as response parameters representing process behaviour. Taper cylindrical sonotrode is designed and manufactured as amplitude of propagated sound wave is inversely proportional to the cross-sectional area in solids. The shape of the tool is designed integral at the end of the sonotrode. Sonotrode with and approximate gain of 3 is designed using CARD (Computer Aided Resonator Design) software. The cross-section of the tool and the amplitude variation along length is shown in Figure 1. The manufacturing drawing produced based on this design is shown in Figure 2. @IJAERD-2015, All rights Reserved

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406

Figure 1. Blanking Sonotrode & Tool Shape with Amplitude Variation

Figure 2. Production Drawing for Blanking Tool The experimental procedure for producing slits in common glass using ultrasonic machining is described as under.

1) 2) 3) 4) 5) 6) 7) 8) 9)

Measure the weight of glass sheet of thickness corresponding to the trial.

Mount the glass sheet in molten wax in petri-dish with aluminium foil at its bottom and allow wax to cure.

Start slurry circulation and adjust the flow.

Set the control parameters and start vibrations using foot operated switch.

Machining is completed when through cut is obtained.

Machining time is recorded using stop watch.

Switch off slurry pump and clean the workpiece using Acetone.

Remove workpiece from petri-dish by reheating wax.

Measure the weight of glass sheet with the slit.

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406 The material removed during the slitting process is determined by subtracting the mass of glass sheet after machining from the mass of sheet before machining. The MRR is then obtained in terms of volumetric material removal rate considering density of common glass as 2.5 gms/cc. OC is calculated considering the tool thickness of 0.38 mm at the cutting edge as the ideal dimension required and evaluating half of the difference between the largest widths of slit and the ideal dimension. Taper is calculated as a ratio of the half of difference between the top and bottom width of the slit produced to the thickness of the glass sheet. The experimental results are listed in Table 2.

Table 2 Experimental Results Thickness Pressure MRR Overcut Sr.No Amplitude Taper mm bar mm3/min Mm 1 1.23 70% 0.5 0.04071 0.10148 0.04125 2 1.23 70% 2 0.0454 0.11873 0.04827 3 1.23 70% 3.5 0.04876 0.13825 0.0562 4 1.23 80% 0.5 0.05336 0.14405 0.05856 5 1.23 80% 2 0.06241 0.1459 0.05931 6 1.23 80% 3.5 0.07383 0.15535 0.06316 7 1.23 90% 0.5 0.07483 0.15618 0.06348 8 1.23 90% 2 0.08701 0.16358 0.06647 9 1.23 90% 3.5 0.09734 0.17268 0.07018 10 1.64 70% 0.5 0.0257 0.1365 0.04161 11 1.64 70% 2 0.02877 0.14545 0.04434 12 1.64 70% 3.5 0.03327 0.1532 0.04671 13 1.64 80% 0.5 0.03081 0.15628 0.04769 14 1.64 80% 2 0.03703 0.1691 0.05156 15 1.64 80% 3.5 0.04342 0.17683 0.05392 16 1.64 90% 0.5 0.05025 0.18463 0.0563 17 1.64 90% 2 0.05416 0.18575 0.05664 18 1.64 90% 3.5 0.05678 0.20065 0.06117 19 3.12 70% 0.5 0.02237 0.1483 0.02377 20 3.12 70% 2 0.02853 0.1585 0.0254 21 3.12 70% 3.5 0.03 0.15933 0.02554 22 3.12 80% 0.5 0.02 0.1712 0.02744 23 3.12 80% 2 0.03 0.18383 0.02947 24 3.12 80% 3.5 0.03 0.19255 0.03085 25 3.12 90% 0.5 0.02722 0.21778 0.0349 26 3.12 90% 2 0.03256 0.21843 0.03423 27 3.12 90% 3.5 0.04152 0.23498 0.03684 III. GRA OPTIMIZATION 3.1 GRA Procedure GRA is an effective method for solving the complicated interrelationship among the multiple designated performance characteristics. It also provides an efficient and effective solution to multi-input and discrete data problems.

In this method, the complex multiple response optimization problem can be simplified into optimization of single response grey relational grade. The procedure for determining the grey relational grade is shown in flow chart Figure 5 [9].

Figure 5. Steps to Determine GRG [9] @IJAERD-2015, All rights Reserved

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406 Data pre-processing: If the number of experiments is “mâ€? and the number of response (i.e. performance characteristics) is “n then the ith experiment can be expressed as Yi = (yi1, yi2, ‌.., yij, ‌.., yin) in decision matrix form, where yij is the performance value (or measure of performance) of response j (j = 1, 2, ‌.., n) for experiment i (i = 1, 2, ‌.., m). The general form of decision matrix D is given as,

ďƒŠ y1l ďƒŞ ... ďƒŞ D  ďƒŞ yil ďƒŞ ďƒŞ ... ďƒŞ yml ďƒŤ

... y1 j ... ... ... yij ... ... ... ymj

... y1n ďƒš ... ... ďƒşďƒş ... yin ďƒş ďƒş ... ... ďƒş ... ymn ďƒşďƒť

The term Yi can be translated into the comparability sequence Xi = (xi1, xi2‌ xij‌ xin) where xij is the normalized value of yij for the response j (j = 1, 2‌ n) of experiment i (i = 1, 2‌ m). After normalization, decision matrix D becomes normalization matrix D’ is given as follows.

ďƒŠ x1l ďƒŞ ... ďƒŞ D'  ďƒŞ xil ďƒŞ ďƒŞ ... ďƒŞ xml ďƒŤ

... x1 j ... ... ... xij ... ... ... xmj

... x1n ďƒš ... ... ďƒşďƒş ... xin ďƒş ďƒş ... ... ďƒş ... xmn ďƒşďƒť

The normalized values xij are determined by use of following equation. These are for beneficial type, nonbeneficial type and target value type responses.

1. If the expectancy of the response is larger-the-better (i.e. beneficial response), then it is expressed by Equation 1.

(1) 2.

If the expectancy of the response is smaller-the-better (i.e. non-beneficial response), then it si determined by using Equation 2.

(2)

3.

If the expectancy of the response is nominal-the-best (i.e. closer to the desired value or target value), then it is expressed by Equation 3.

(3)

where Yj* is closer to the desired value of jth response.

Reference sequence: In comparability sequence all performance values are scaled to [0, 1]. For a response j of experiment i, if the value xij is equal to 1 or nearer to 1 then the value for any experiment, then the performance of experiment i is considered as best for the response j. The reference sequence X is defined as (x1, x2, ‌.., xj, ‌.., xn) = (1, 1, ‌.., 1, ‌..,, 1), where xj is the reference value for jth response and it aims to find the experiment whose comparability sequence is closest to the reference sequence.

Grey relational coefficients: Grey relational coefficient is used for determining how close xij is to xj. The larger the grey relational coefficient, the closer xij and xj are. The grey relational coefficient can be calculated using Eq. 4-Eq. 7.

(4) For i = 1, 2‌ m and j = 1, 2... n Where,

� = the grey relational coefficient (5) (6) (7)

The purpose of distinguishing coefficient is to expand or compressed the range of the grey relational coefficient.

Different distinguishing coefficient may lead to different solution results. Generally a value of 0.5 for distinguishing coefficient is preferred.

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406 Grey relational grades: The measurement formula for quantification in grey relational space is called grey relational grade. A grey relational grade (grey relational degree) is a weighted sum of grey relational coefficients and it can be calculated using Equation 8.

i   j 1 w j .ij n

i = 1, 2… m and j = 1, 2… n

(8)

where i is the grey relational grade between comparability sequence Xi and reference sequence Xn. It represents correlation between the reference sequence and the comparability sequence, wj is the weight of response j and depends on decision maker’s judgment.

3.2 Optimization Using Grey Analysis As discussed in section 3.1 step 1, an ideal sequence (Xij = 1, j = 1, 2 . . . 9) for MRR, OC and taper is generated as shown in Table 2 which also shows the experimentally obtained values of these response parameters. Equation 1 is applied for MRR and Equation 2 for OC and taper both of which should be minimized. Grey relational coefficients are calculated taking value of distinguishing coefficient as 0.5 using Equation 4-Equation 7. Table 3 shows the grey relational coefficients for each of the measured responses for ultrasonic slitting of glass. Ultrasonic machining may be used for rough cutting where accuracy may not be as important as the MRR. It can also be used for semi-finishing where equal weight has to be given to all response parameters. USM can be used to obtain final component by finish cutting using small weights for MRR and relatively higher importance to dimensional accuracy in terms of OC and taper. Grey optimization is conducted for all the three cutting scenarios. In case of optimization for rough cutting, value of 0.65 is selected as weight for MRR and OC and taper are given weights of 0.20 and 0.15 respectively. OC being given larger weightage to identify the fact that dimensional accuracy also controls the taper on the feature produced. In case of semifinish cutting, to balance between MRR and limit the ROC and taper simultaneously, MRR is assigned a weight of 0.34 and OC and taper are given weightage of 0.33 each. In case of finishing cuts, 80% weightage is given to limiting of OC and taper for dimensional accuracy with OC and taper being given weights of 0.5 & 0.3 respectively and MRR is given a low weight of 0.2. These weights are used to calculate grey relational grade using Equation 8 and its order as shown for roughing case in Table 3 for ultrasonic blanking. Similar to roughing case, grey relational grades are found for semifinishing and finishing cases as well and given ranks in descending order of the grade. These results are listed in Table 4.

Table 2. Sequence of Performance Characteristics after Data Pre-Processing SN

T

A

P

70% 70% 70% 80% 80% 80% 90% 90% 90% 70% 70% 70% 80% 80% 80% 90% 90% 90% 70% 70% 70% 80% 80% 80% 90% 90% 90% Max. Min. Diff.

0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5 0.5 2 3.5

Ideal--> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

1.23 1.23 1.23 1.23 1.23 1.23 1.23 1.23 1.23 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.64 1.64 3.12 3.12 3.12 3.12 3.12 3.12 3.12 3.12 3.12

MRR 0.0973 0.04071 0.0454 0.04876 0.05336 0.06241 0.07383 0.07483 0.08701 0.09734 0.0257 0.02877 0.03327 0.03081 0.03703 0.04342 0.05025 0.05416 0.05678 0.02237 0.02853 0.03 0.02 0.03 0.03 0.02722 0.03256 0.04152 0.097344 0.022375 0.074969

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OC 0.1015 0.10148 0.11873 0.13825 0.14405 0.1459 0.15535 0.15618 0.16358 0.17268 0.1365 0.14545 0.1532 0.15628 0.1691 0.17683 0.18463 0.18575 0.20065 0.1483 0.1585 0.15933 0.1712 0.18383 0.19255 0.21778 0.21843 0.23498 0.234975 0.101475 0.133500

Taper 0.0238 0.04125 0.04827 0.0562 0.05856 0.05931 0.06316 0.06348 0.06647 0.07018 0.04161 0.04434 0.04671 0.04769 0.05156 0.05392 0.0563 0.05664 0.06117 0.02377 0.0254 0.02554 0.02744 0.02947 0.03085 0.0349 0.03423 0.03684 0.070181 0.023765 0.046415

xMRR 1.0000 0.2446 0.3072 0.3519 0.4133 0.5341 0.6864 0.6996 0.8621 1.0000 0.0444 0.0853 0.1454 0.1125 0.1955 0.2807 0.3718 0.4239 0.4589 0.0000 0.0821 0.1356 0.0129 0.0719 0.1501 0.0646 0.1359 0.2554 1.0000 0.0000 0.7015

xOC 1.0000 1.0000 0.8708 0.7245 0.6811 0.6672 0.5964 0.5903 0.5348 0.4667 0.7376 0.6706 0.6125 0.5895 0.4934 0.4356 0.3772 0.3687 0.2571 0.6493 0.5728 0.5667 0.4777 0.3831 0.3178 0.1288 0.1240 0.0000 0.0000 1.0000 0.7601

xTaper 1.0000 0.6234 0.4721 0.3011 0.2504 0.2343 0.1513 0.1443 0.0799 0.0000 0.6156 0.5567 0.5058 0.4846 0.4011 0.3504 0.2991 0.2917 0.1942 1.0000 0.9647 0.9619 0.9208 0.8772 0.8473 0.7601 0.7746 0.7182 0.0000 1.0000 0.5120

MRR 0.0000 0.7554 0.6928 0.6481 0.5867 0.4659 0.3136 0.3004 0.1379 0.0000 0.9556 0.9147 0.8546 0.8875 0.8045 0.7193 0.6282 0.5761 0.5411 1.0000 0.9179 0.8644 0.9871 0.9281 0.8499 0.9354 0.8641 0.7446 0.0000 1.0000 0.2985

OC 0.0000 0.0000 0.1292 0.2755 0.3189 0.3328 0.4036 0.4097 0.4652 0.5333 0.2624 0.3294 0.3875 0.4105 0.5066 0.5644 0.6228 0.6313 0.7429 0.3507 0.4272 0.4333 0.5223 0.6169 0.6822 0.8712 0.8760 1.0000 1.0000 0.0000 0.2399

Taper 0.0000 0.3766 0.5279 0.6989 0.7496 0.7657 0.8487 0.8557 0.9201 1.0000 0.3844 0.4433 0.4942 0.5154 0.5989 0.6496 0.7009 0.7083 0.8058 0.0000 0.0353 0.0381 0.0792 0.1228 0.1527 0.2399 0.2254 0.2818 1.0000 0.0000 0.4880

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406 Table 3. Grey Relational Coefficients & Grey Relational Grades for Roughing Sr. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

 MRR 0.65 0.3983 0.4192 0.4355 0.4601 0.5176 0.6145 0.6247 0.7838 1.0000 0.3435 0.3534 0.3691 0.3604 0.3833 0.4101 0.4432 0.4646 0.4803 0.3333 0.3526 0.3664 0.3362 0.3501 0.3704 0.3483 0.3665 0.4017

 OC 0.20 1.0000 0.7946 0.6448 0.6106 0.6004 0.5534 0.5496 0.5180 0.4839 0.6559 0.6028 0.5634 0.5492 0.4967 0.4697 0.4453 0.4420 0.4023 0.5877 0.5393 0.5357 0.4891 0.4477 0.4229 0.3647 0.3634 0.3333

T 0.15 0.5704 0.4864 0.4171 0.4001 0.3950 0.3707 0.3688 0.3521 0.3333 0.5654 0.5301 0.5029 0.4924 0.4550 0.4349 0.4163 0.4138 0.3829 1.0000 0.9341 0.9291 0.8632 0.8028 0.7660 0.6758 0.6892 0.6396

Grade

Rank

0.5444 0.5044 0.4746 0.4812 0.5158 0.5657 0.5713 0.6659 0.7968 0.4393 0.4298 0.4280 0.4179 0.4167 0.4257 0.4396 0.4525 0.4501 0.4842 0.4772 0.4847 0.4459 0.4375 0.4402 0.4007 0.4143 0.4237

5 7 12 10 6 4 3 2 1 18 20 21 24 25 22 17 13 14 9 11 8 15 19 16 27 26 23

Table 4. Grey Relational Grades for Various Ultrasonic Slitting Conditions S. N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Roughing Grade Rank 0.5444 5 0.5044 7 0.4746 12 0.4812 10 0.5158 6 0.5657 4 0.5713 3 0.6659 2 0.7968 1 0.4393 18 0.4298 20 0.4280 21 0.4179 24 0.4167 25 0.4257 22 0.4396 17 0.4525 13 0.4501 14 0.4842 9 0.4772 11 0.4847 8 0.4459 15 0.4375 19 0.4402 16 0.4007 27 0.4143 26 0.4237 23

Semi-Finishing Grade Rank 0.6562 1 0.5668 6 0.4991 15 0.4903 17 0.5044 14 0.5129 13 0.5144 12 0.5513 8 0.6057 5 0.5216 10 0.4954 16 0.4785 18 0.4673 20 0.4450 23 0.4382 25 0.4349 26 0.4401 24 0.4218 27 0.6404 2 0.6087 4 0.6104 3 0.5629 7 0.5335 9 0.5198 11 0.4629 21 0.4730 19 0.4582 22

Finishing Grade Rank 0.7508 1 0.6271 3 0.5346 10 0.5173 14 0.5222 12 0.5108 16 0.5104 17 0.5214 13 0.5419 8 0.5662 7 0.5311 11 0.5064 18 0.4944 19 0.4615 21 0.4474 23 0.4362 26 0.4381 25 0.4121 27 0.6605 2 0.6204 4 0.6199 5 0.5708 6 0.5347 9 0.5154 15 0.4547 22 0.4618 20 0.4389 24

IV. RESULTS & DISCUSSION From the listing of grey relational grades in Table 4 it is observed that for ultrasonic slitting of common glass, in case of roughing the best rank is attributed to DOE serial 9 which relates to lowest thickness and maximum pressure and maximum amplitude. While in case of semi-finishing as well as finishing the best rank is attributed to DOE serial 1 which is the combination of lowest thickness, lowest pressure and lowest amplitude.

This is matching with the experimental findings and subsequent analysis showing that MRR is higher for lower thickness values and higher pressure and amplitude values. In case of semi-finishing and finishing operations the effective contribution of MRR to the grade is lower as compared to the combined effect of OC and taper which leads to the same combination being selected as the best for semi-finishing and finishing cases. These combinations are indicated in bold in Table 4.

(1) (2) (3) (4) (5)

[1] [2]

[3] [4]

IV. CONCLUSION Following major conclusions can be drawn from the attempt to apply GRA to ultrasonic slitting of glass, GRA procedure converts decision making involving multiple performance characteristics into a decision regarding single performance indicator in terms of the grey relational grade using suitable weights.

Weights should be carefully decided depending upon the machining performance required.

The optimum combination of control variables can be selected by ranking the parameter combinations using GRA procedure.

The combination of lowest thickness, highest pressure and highest amplitude is found optimum for roughing.

The combination of lowest thickness, lowest pressure and lowest amplitude is found optimum for semi-finishing and finishing.

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International Journal of Advance Engineering and Research Development (IJAERD) Volume 2,Issue 12,December -2015,e-ISSN: 2348 - 4470 , print-ISSN:2348-6406 [5] [6] [7]

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